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International Colloquium on Automata, Languages, and Programming

ICALP 1979: Automata, Languages and Programming pp 316–330Cite as

A unique termination theorem for a theory with generalised commutative axioms

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 71))

Abstract

The procedures for deciding the unique termination property of rewriting systems by Knuth and Bendix [1], and Lankford and Ballantyne [2] are generalised to allow for permutative axioms of the form

$$F(F(t,e_1 ),e_2 ) = F(F(t,e_2 ),e_1 )$$

(t,e1,e2 are variable symbols).

These can be thought of as many sorted commutative axioms as they might appear in axiomatic specifications of abstract data types.

A method is presented for deciding the unique termination property of a set of "permutative rewrite rules" having the finite termination property. It relies on "confluence" results of Gerard Huet [4].

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References

  1. D.E.Knuth & P.B.Bendix: Simple Word Problems in Universal Algebras in Computational Problems in Abstract Algebra Ed. J.Leech, Pergamon Press 1970, pp.263–297

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  2. D.S.Lankford & A.M.Ballantyne: Decision Procedures for Simple Equational Theories with a Commutative Axiom: Complete Sets of Commutative Reductions Automatic Theorem Proving Project, Depts. Math. and Comp. Science, University of Texas at Austin; Report #ATP-35

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  3. D.S.Lankford & A.M.Ballantyne: Decision Procedures for Simple Equational Theories with Commutative-Associative Axioms: Complete Sets of Commutative-Associative Reductions As [2], Report #ATP-39

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  4. G.Huet: Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems IRIA-LABORIA, Domaine de Voluceau, F-78150 Rocquencourt France. Preliminary version in 18th IEEE Symposium on Foundations of Computer Science, Oct 1977

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  5. J.A. Robinson: A Machine-Oriented Logic Based on the Resolution Principle. JACM Vol.12, No.1; January 1965; pp.23–41

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Authors and Affiliations

  1. Computer Science Department, University of Edinburgh, UK

    Hans-Josef Jeanrond

Authors
  1. Hans-Josef Jeanrond
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Hermann A. Maurer

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© 1979 Springer-Verlag Berlin Heidelberg

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Jeanrond, HJ. (1979). A unique termination theorem for a theory with generalised commutative axioms. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09510-1_25

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  • DOI: https://doi.org/10.1007/3-540-09510-1_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09510-1

  • Online ISBN: 978-3-540-35168-9

  • eBook Packages: Springer Book Archive

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